Class 4 (4th Engineer) MET 📅 Jan 2025

Exam Question

The loads of a 3-wire, 3-phase system are: (16)

Red line to neutral current = 50 A, power factor of 0.707 (lagging)

Yellow line to neutral current = 40 A, power factor of 0.866 (lagging)

Blue line to neutral current = 40 A, power factor 0.707 (leading)

Determine the value of the current in the neutral wire.

Reference Answer

### Principle of Superposition for Unbalanced Loads
In a 3-phase, 4-wire star-connected system, the current flowing in the neutral wire is the phasor (vector) sum of the currents in the three individual phases (Red, Yellow, and Blue). This is a direct application of Kirchhoff's Current Law at the neutral point, where the algebraic sum of currents entering and leaving the junction is zero.
Mathematically, this is expressed as:
$$ \vec{I_N} = - (\vec{I_R} + \vec{I_Y} + \vec{I_B}) $$

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